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  • 1.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A survey of pointwise interpolation inequalities for integer and fractional derivatives2002In: Acoustics, Mechanics, and the Related Topics of Mathematical Analysis,2002, Singapore: World Scientific , 2002, p. 212-Conference paper (Refereed)
  • 2.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces2002In: Journal of evolution equations (Printed ed.), ISSN 1424-3199, E-ISSN 1424-3202, Vol. 2, no 1, p. 113-125Article in journal (Refereed)
    Abstract [en]

    An elementary proof of the Brezis and Mironescu theorem on the boundedness and continuity of the composition operator: Ws,P(Rn) n W1,sp(Rn) ? Ws,p(Rn) is given. The proof includes the case p = 1.

  • 3.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Characterization of multipliers in pairs of Besov spaces2004In: Operator theoretical methods and applications to mathematical physics / [ed] Israel Gohberg, Antonio F. dos Santos, Frank-Olme Speck, Francisco Sepulveda Teixeira, Basel: Birkhäuser , 2004, 1, p. 365-387Chapter in book (Other academic)
    Abstract [en]

    Devoted to the memory of the applied mathematician Erhard Meister (1930-2001). This work is divided into two parts. Part A contains reminiscences about the life of E Meister. Part B displays the wide range of his scientific interests through eighteen papers with close scientific and personal relations to Erhard Meister

  • 4.
    Maz'ya, Vladimir G.
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Higher regularity in the layer potential theory for lipschitz domains2005In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 54, no 1, p. 99-142Article in journal (Refereed)
    Abstract [en]

    Classical boundary integral equations of the harmonic potential theory on Lipschitz surfaces are studied. We obtain higher fractional Sobolev regularity results for their solutions under sharp conditions on the surface. These results are derived from a theorem on the solvability of auxiliary boundary value problems for the Laplace equation in weighted Sobolev spaces.

  • 5.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces2002In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 195, no 2, p. 230-238Article in journal (Refereed)
    Abstract [en]

    The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: Ws,p ? Lpn/(n-sp) as s ? 1 and s ? n/p. Their result is extended to all values of s ? (0, 1) and is supplied with an elementary proof. The relation is proved. © 2002 Elsevier Science (USA).

  • 6.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the Bourgain, Brezis and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces (vol 195, pg 230, 2002)2003Other (Other academic)
  • 7.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the brezis and mironescu conjecture concerning a Gagliardo-Nirenberg inequality for fractional Sobolev norms2002In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 81, no 9, p. 877-884Article in journal (Refereed)
    Abstract [en]

    We prove the Gagliardo-Nirenberg type inequality where 0 < ? < 1, 0 < s < 1, 1 < p < 8, and ?u? Ws,p is the seminorm in the fractional Sobolev space Ws,p (Rn). The dependence of the constant factor in the right-hand side on each of the parameters s, ?, and p is precise in a sense. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

  • 8.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Sharp pointwise interpolation inequalities for derivatives2002In: Functional analysis and its applications, ISSN 0016-2663, E-ISSN 1573-8485, Vol. 36, no 1, p. 30-48Article in journal (Refereed)
    Abstract [en]

    We prove new point-wise inequalities involving the gradient of a function u is an element of C-1(R-n), the modulus of continuity w of the gradient delu, and a certain maximal function M(lozenge)u and show that these inequalities are sharp. A simple particular case corresponding to n = 1 and w(r) = r is the Landau type inequality [GRAPHIC] where the constant 8/3 is best possible and [GRAPHIC]

  • 9.
    Maz´ya, Vladimir
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mitrea, M
    University of Missouri.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO2009In: FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, ISSN 0016-2663, Vol. 43, no 3, p. 217-235Article in journal (Refereed)
    Abstract [en]

    The goal of this work is to study the inhomogeneous Dirichlet problem for the Stokes system in a Lipschitz domain Omega aS dagger a"e (n) , na (c) 3/42. Our main result is that this problem is well posed in Besov-Triebel-Lizorkin spaces, provided that the unit normal nu to Omega has small mean oscillation.

  • 10.
    Maz´ya, Vladimir
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mitrea, Marius
    University of Missouri at Columbia.
    Shaposhnikova, Tatiana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients2010In: Journal d’Analyse Mathématique, ISSN 0021-7670, Vol. 110, no 1, p. 167-239Article in journal (Refereed)
    Abstract [en]

    We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

  • 11.
    Mazya, Vladimir
    et al.
    University of Liverpool.
    Shaposhnikova, Tatiana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Brezis-Gallouet-Wainger type inequality for irregular domains2011In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 56, no 10, p. 991-1002Article in journal (Refereed)
    Abstract [en]

    A Brezis–Gallouet–Wainger logarithmic interpolation-embedding inequality is proved for various classes of irregular domains, in particular, for power cusps and λ-John domains.

  • 12.
    Maz´ya, Vladimir
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A Collection of sharp dilation invariant integral inequalities for differentiable functions2008In: Sobolev Spaces in Mathematics I. Sobolev Type Inequalities / [ed] Vladimir Maz’ya, Berlin, Heidelberg: Springer , 2008, p. 223-248Chapter in book (Other academic)
    Abstract [en]

    Presentation of new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics

    • The authors and editors are world-renowned specialists, working in different countries
    • Publication on the centenary of Sobolev’s birth with two short biographical articles and unique archive photos of S. Sobolev which have not yet been published in the English-language literature

    This volume is dedicated to the centenary of the outstanding mathematician of the XXth century Sergey Sobolev and, in a sense, to his celebrated work On a theorem of functional analysis published in 1938, exactly 70 years ago, where the original Sobolev inequality was proved. This double event is a good case to gather experts for presenting the latest results on the study of Sobolev inequalities which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc. The volume opens with a nice survey reminiscence My Love Affair with the Sobolev Inequality by David R. Adams.

  • 13.
    Maz'ya, Vladimir
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A collection of sharp dilation invariant integral inequalities for differentiable functions2009In: Sobolev spaces in mathematics. I / [ed] Vladimir Maz'ya, Springer , 2009, vol. 8, p. 223-247Chapter in book (Other (popular science, discussion, etc.))
  • 14.
    Maz´ya, Vladimir
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Jacques Hadamard, Legend of Mathematics2008Book (Other academic)
  • 15.
    Mazya, Vladimir
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains2011In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615, Vol. 1, no 1, p. 33-77Article in journal (Refereed)
    Abstract [en]

    This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains. Asymptotic properties of solutions at a point of a Lipschitz boundary are also discussed.

  • 16.
    Maz´ya, Vladimir
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Theory of Sobolev Multipliers: with Applications to Differential and Integral Operators2008Book (Other academic)
    Abstract [en]

      The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results. Part I is devoted to the theory of multipliers and encloses the following topics: trace inequalities, analytic characterization of multipliers, relations between spaces of Sobolev multipliers and other function spaces, maximal subalgebras of multiplier spaces, traces and extensions of multipliers, essential norm and compactness of multipliers, and miscellaneous properties of multipliers. Part II concerns several applications of this theory: continuity and compactness of differential operators in pairs of Sobolev spaces, multipliers as solutions to linear and quasilinear elliptic equations, higher regularity in the single and double layer potential theory for Lipschitz domains, regularity of the boundary in $L_p$-theory of elliptic boundary value problems, and singular integral operators in Sobolev spaces.

  • 17.
    Shaposhnikova, Tatiana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Von Neumann with the Devil, translation of a play by L. Gårding from Swedish to Russian2009In: Algebra and Analyses, ISSN 0231-0852, Vol. 21, no 3, p. 1-5Article in journal (Other (popular science, discussion, etc.))
  • 18.
    Shaposhnikova, Tatyana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Application of Sobolev multipliers in a non-smooth L_p theory of classical boundary integral equations2004In: Boundary Integral Methods: Theory and Applications,2004, 2004Conference paper (Refereed)
  • 19.
    Shaposhnikova, Tatyana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Description of Pointwise Multipliers in Pairs of Besov Spaces B-1(k)(R-n)2009In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, ISSN 0232-2064, Vol. 28, no 1, p. 67-85Article in journal (Refereed)
    Abstract [en]

    Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space B-1(m)(R-n) into the Besov space B-1(l)(R-n) with integer l and m, 0 < l <= m, are found. It is shown that multipliers between B-1(m)(R-n) and B-1(l)(R-n) form the space of traces of multipliers between the Sobolev classes W-1(m+1)(R-+(n+1)) and W-1(l+1)(R-+(n+1)).

  • 20.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary2009Conference paper (Refereed)
  • 21.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Dirichlet Problem in Lipschitz Domains with Boundary Data in Besov Spaces for Higher Order Elliptic Systems2006In: Geometric Methods in Nonlinear PDEs and Free Boundary Problems,2006, 2006, p. 11-11Conference paper (Other academic)
  • 22.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Harmonic Potentials Theory in Besov Spaces for Lipschitz Domains2006In: International Conference on Complex Analysis and Potential Theory, Satellite to the ICM 2006,2006, 2006, p. 19-19Conference paper (Other academic)
  • 23.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Higher regularity in the classical layer potential theory for Lipschitz domains2008In: Analysis, PDEs and Applications on the occasion of the 70th birthday of Vladimir Mazya,2008, 2008, p. 44-44Conference paper (Other academic)
  • 24.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Higher regularity in the classical layer potential theory for Lipschitz domains2009Conference paper (Refereed)
  • 25.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Higher regularity in the layer potential thaory2005In: Conference on Operator Theory, Function Spaces and Applications,2005, 2005, p. 29-30Conference paper (Other academic)
  • 26.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Higher regularity in the theory of harmonic layer potentials2006In: AMS Meeting,2006, 2006, p. 47-47Conference paper (Other academic)
  • 27.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Inequality for entire functions involving their maximum modulus and maximum term2012In: Rendiconti Lincei - Matematica e Applicazioni, ISSN 1120-6330, E-ISSN 1720-0768, Vol. 23, no 3, p. 259-265Article in journal (Refereed)
    Abstract [en]

    An estimate of the Wiman-Valiron type for a maximum modulus on a polydisk of an entire function of several complex variables is obtained. The estimate contains a weight function involved also in the calculation of the radius of the admissible ball.

  • 28.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Multipliers in Besov spaces with applications to differential operators2008In: Analysis, Operator Theory and Applications,2008, 2008Conference paper (Other academic)
  • 29.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Multipliers in spaces of Sobolev type and their applications2008In: Nordic-Russian Symposium in honour of Vladimir Mazya,2008, 2008, p. 19-19Conference paper (Other academic)
  • 30.
    Shaposhnikova, Tatyana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the boundedness of the composition operator in fractional Sobolev spaces2003In: Operator Theory in Analysis and Engineering,2003, 2003Conference paper (Other academic)
  • 31.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Pointwise Interpolation Inequalities for Fractional Derivatives and Their Applications2006In: Workshop on Function Spaces and Differential Equations,2006, 2006Conference paper (Other academic)
  • 32.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Pointwise multipliers of differentiable finctions with applications to PDEs2007In: 1027th Meeting of the American Mathematical Society,2007, 2007, p. 54-54Conference paper (Other academic)
  • 33.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Three high-stakes math exams2005Other (Other academic)
    Abstract [en]

    [No abstract available]

  • 34.
    Shaposhnikova, Tatyana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Von Neumann with the Devil, a play by Lars Gårding, translated into Russian by T. Shaposhnikova2009In: Algebra i Analiz, Vol. 21, no 5, p. 222-226Article in journal (Refereed)
1 - 34 of 34
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